Driven Imposters: Controlling Expectations in Many-Body Systems

Abstract

We present a framework for controlling the observables of a general correlated electron system driven by an incident laser field. The approach provides a prescription for the driving required to generate an arbitrary predetermined evolution for the expectation value of a chosen observable, together with a constraint on the maximum size of this expectation. To demonstrate this, we determine the laser fields required to exactly control the current in a Fermi-Hubbard system under a range of model parameters, fully controlling the non-linear high-harmonic generation and optically observed electron dynamics in the system. This is achieved for both the uncorrelated metallic-like state and deep in the strongly-correlated Mott insulating regime, flipping the optical responses of the two systems so as to mimic the other, creating 'driven imposters'. We also present a general framework for the control of other dynamical variables, opening a new route for the design of driven materials with customized properties.

Towards Single Atom Computing via High Harmonic Generation

“…An analogous physical property is present in HHG systems (see Fig. 1), where it has been shown [36][37][38] that regardless of the physical specifics of the system, there always exists an incident laser field (input) that will induce a desired optical response (output). For this reason, a single atom undergoing HHG provides an appealing platform for computation.…”

“…HHG occurs when a short and intense laser pulse generates responses of up to ≈ 100 times the frequency of the incident field. It has been shown that both atomic [36] and solid-state [37,38] systems exhibiting HHG also possess the equally desirable property of universality. In a computational context, universality implies that regardless of architecture, any output result can be obtained by suitable input data and software.…”

High harmonic generation in two-dimensional Mott insulators

“…However, the interplay of these temporal non-linear strongfield effects with non-perturbative strong electronic correlations, fundamentally changes the optical response of a material and enters a rich emergent regime of novel collective phenomena. This offers the possibility of emission of even higher harmonics due to coupling with these many-body interactions, and the proposal of engineering of photo-induced correlated phases [19][20][21][22]. However, HHG and driving fields in strongly correlated materials is far from understood, and is emerging as a key research challenge in computational non-equilibrium science.…”

Optical Indistinguishability via Twinning Fields

“…Using tracking quantum control [14][15][16][17][18][19][20][21], recent work has demonstrated that almost arbitrary control over the optical response of a large class of solid-state systems can be achieved [22,23]. One consequence of this is that two specially tailored driving fields will induce an identical response from two distinct systems.…”

“…Consider a typical example of an optically driven current. The current operator Ĵ(k) is defined from a continuity equation for the electron density [22,23]. Provided all number operators njσ = ĉ † jσ ĉjσ commute with Û (k) , each system's current operator has the form [45]:…”